# Hwk-8 - and or replacing the machine, which costs c R and...

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Homework 8 Due: November 20, 2008 1. Exercise #6 on page 120 of Denardo’s book. 2. Problem #11 on page 131 of Denardo’s book. 3. (Equipment replacement problem) A piece of equipment (machine) is observed to be in some state i at the beginning of each of N periods, i = 1 ,...,K . Let α denote the one-period discount factor. State i = 1 corresponds to a new machine, while state i = K corresponds an inoperable ma- chine. Intermediate states represent gradual states of ineﬃciency. There are two decisions possible at the beginning of each period: “doing nothing” and just continue to operate the existing machine;
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Unformatted text preview: and or replacing the machine, which costs c R and occurs instantaneously which corresponds to making an immediate transition to state 1. Machine in operation for one period in state i costs c ( i ), and the state of the machine at the beginning of the next period becomes j with probability p ij , j = i,i +1 ,...,K . The objective is to minimize the expected total discounted cost from period 1 to period N . Formulate this problem as a Dynamic programming to characterize the optimal operating strategy. 1...
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## This note was uploaded on 03/16/2012 for the course IEOR 466 taught by Professor Richard during the Spring '12 term at Columbia.

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